In our analysis, the mini-jet model of QCD can be then employed for the photoproduction cross sections with the inclusion of the vector meson dominance and the saturation effects for total hadronic and photonic cross sections at a high energy regime.
The decomposition of the Fourier function into the number of weighted component modes, associated with hadronic cross sections was introduced in Ref. [1]}.
The total inelastic cross section can be transformed through the energy-weighted correlation Fourier transform of the cross section, considered as a spatially localized function,
\((k)=\frac{1}{\sqrt{2\pi }}\! \int _{\mathbb {R}}(x)e^{ikx} d x.\) 
